104 



Dr. J. H. Vincent on a Numerical 



includes the numerics of all known elements excepting hydro- 

 gen," a numeric being an atomic weighty. He arranged all the 

 atomic weights in ascending order of magnitude, and without 

 altering the order, these were divided into sixteen groups by 

 trial. The number j» is the same integer for each group. The 

 value of x was obtained by arithmetic for each element. 

 Mills restricted himself only by having x always either an 

 integer or infinity, and then chose its value so that the calcu- 

 lated atomic weight should be as near as possible to the expe- 

 rimental value. An example of a group is given below to 

 illustrate tbe method. 



Group III. 



y — 45 — 15(*9375)- 





, 



?/■ 



y < ale. 



p 



1 



2 



7 



11 

 17 

 J2 



31-C8 

 3o-37 

 39-02 

 3990 

 43-98 



.094 

 31-82 

 35-45 

 38-92 

 39 99 

 44 00 



s 



CI 



K 



Ca 



So 



When we consider the large amount of choice involved in 

 the compilation of such a table, it is not at all surprising 

 that the numbers in the last two columns of the above table 

 agree closely ; indeed there seems no reason to doubt that 

 by some such arbitrary process the numbers in the last two 

 columns could be made to agree to any required degree of 

 accuracy. 



To find the atomic weight of an element by this method 

 one would require to know the group in which the element 

 had been placed, the value of x assigned to the element, as 

 well as the constants occurring in the equation. 



While regarding the work as leading to the conclusion that 

 there might be an infinite number of elements having atomic 

 weights less than about 240, Mills considered that tin? value 

 was the upper limit. 



The formulae are subsequently derive! by the contemplation 

 of a hot nebular mass of primitive substance which, while 

 cooling freely in space, gives birth to polymers of this 



